AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta\) are the roots of the equation \(x^2+b x+c=0\) satisfying the conditions \(\alpha+\beta=5\) and \(\alpha^3+\beta^3=60\), then \(3 c+2=\)
- A \(2b\)
- B \(3b\)
- C \(-3b\)
- D \(-2b\)
Answer & Solution
Correct Answer
(C) \(-3b\)
Step-by-step Solution
Detailed explanation
\(\alpha+\beta=-b \Rightarrow 5=-b \Rightarrow b=-5\) \(\alpha^3+\beta^3=(\alpha+\beta)((\alpha+\beta)^2-3\alpha\beta)\) \(60=5(5^2-3\alpha\beta) \Rightarrow 12=25-3\alpha\beta \Rightarrow 3\alpha\beta=13 \Rightarrow \alpha\beta=\frac{13}{3}\)…
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